A previous random sample of 4000 U.S. citizens yielded 2250 who are in favor of gun control legislation. How many citizens would need to be sampled for a 95% confidence interval to estimate the true proportion within 2%
Solution :
Given that,
n = 4000
x = 2250
= 2250 / 4000 = 0.5625
1 - = 1 - 0.5625 = 0.4375
margin of error = E = 2% = 0.02
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2 = Z0.025 = 1.96
sample size = n = (Z / 2 / E )2 * * (1 - )
= (1.96 / 0.02)2 * 0.5625 * 0.4375
= 2363.48
= 2364
2364 citizens would need to be sampled .
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